C.E. Evans wrote:
perhaps a TOS spinoff could just be one aboard a different kind of Starfleet vessel--a old transport ship that's smaller, slower, and less armed than the Enterprise
The Starfleet freighter U.S.S. Huron
from TAS' "The Pirates of Orion"
sort of fit your description, as it was certainly not as large, fast or battle-capable as the Enterprise
, had a smaller crew (only three were seen). A ship of its class would make the crew feel more isolated in the far reaches of space than the large, well-supplied Constitution class ship.
Perhaps you would see a focus on personal stories more than the interests of Starfleet.